Injectors in fitting sets of finite groups

On Injectors of a Hartley Set of a Finite Group

“…Hence, if F = T r F (G), then the theorem of Anderson [1] and the theorem of Fischer, Gaschütz and Hartley [4] are Corollaries of the theorem of Shemetkov [15]. Vorob'ev and Semenov [17] proved that for every set π of primes and every Fitting set F of π-soluble group G, G possesses an F-injector and any two F-injectors are conjugate if F is π-saturated, i.e. F = {H ≤ G : H/H F ∈ E π ′ }.…”